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# Help needed on C3 question watch

1. Hi guys,
I have been trying to answer this C3 question for so long but i keep getting stuck at one particular point; could someone please help me
I haven't included part a and part b as I'm pretty sure they're not relevant.

The function f is defined by f(x)=3-2e^-x

The equation f(t)=ke^t , where k is a positive constant, has exactly one real solution.
c) Find the value of k

This is what I've done so far:

*when x=t, y=ke^t
therefore f(t)=3-2e^-t
therefore ke^t=3-2e^-t

* multiply by e^t and rearrange to get a quadratic equation
ke^2t -3e^t +2=0

* let x=e^t
therefore kx^2 -3x+2 =0

And then i have no idea how to factorise to find what k is, please help me understand what to do next.
I'm pretty sure the fact that they say "the equation has exactly one real solution" means something but I'm not sure what.
Thank you so much
2. (Original post by Deema18)
Hi guys,
I have been trying to answer this C3 question for so long but i keep getting stuck at one particular point; could someone please help me
I haven't included part a and part b as I'm pretty sure they're not relevant.

The function f is defined by f(x)=3-2e^-x

The equation f(t)=ke^t , where k is a positive constant, has exactly one real solution.
c) Find the value of k

This is what I've done so far:

*when x=t, y=ke^t
therefore f(t)=3-2e^-t
therefore ke^t=3-2e^-t

* multiply by e^t and rearrange to get a quadratic equation
ke^2t -3e^t +2=0

* let x=e^t
therefore kx^2 -3x+2 =0

And then i have no idea how to factorise to find what k is, please help me understand what to do next.
I'm pretty sure the fact that they say "the equation has exactly one real solution" means something but I'm not sure what.
Thank you so much
Discriminant=0?
3. (Original post by lerjj)
Discriminant=0?

Oh my gosh!!! That makes so much sense!!! I had completely forgot about all the C1 knowledge ^^
Thank you so much!

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